{
  "id": "1111.6406",
  "version": "v3",
  "published": "2011-11-28T11:14:21.000Z",
  "updated": "2013-03-26T11:44:12.000Z",
  "title": "Discrete components in restriction of unitary representations of rank one semisimple Lie groups",
  "authors": [
    "Genkai Zhang"
  ],
  "comment": "Revised version",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider spherical principal series representations of the semisimple Lie group of rank one $G=SO(n, 1; \\mathbb K)$, $\\mathbb K=\\br, \\bc, \\bh$. There is a family of unitarizable representations $\\pi_{\\nu}$ of $G$ for $\\nu$ in an interval on $\\mathbb R^+$, the so-called complementary series, and subquotient or subrepresentations of $G$ for $\\nu$ being negative integers. We consider the restriction of $(\\pi_{\\nu}, G)$ under the subgroup $H=SO(n-1, 1; \\mathbb K)$. We prove the appearing of discrete components. The corresponding results for the exceptional Lie group $F_{4(-20)}$ and its subgroup $Spin(8,1)$ are also obtained.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-26T11:44:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie group",
      "discrete components",
      "unitary representations",
      "restriction",
      "exceptional lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6406Z"
    }
  }
}